Simplify the following expression: $ a = \dfrac{5z - 3}{-6z + 9} - \dfrac{-9}{4} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{5z - 3}{-6z + 9} \times \dfrac{4}{4} = \dfrac{20z - 12}{-24z + 36} $ Multiply the second expression by $\dfrac{-6z + 9}{-6z + 9}$ $ \dfrac{-9}{4} \times \dfrac{-6z + 9}{-6z + 9} = \dfrac{54z - 81}{-24z + 36} $ Therefore $ a = \dfrac{20z - 12}{-24z + 36} - \dfrac{54z - 81}{-24z + 36} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{20z - 12 - (54z - 81) }{-24z + 36} $ Distribute the negative sign: $a = \dfrac{20z - 12 - 54z + 81}{-24z + 36}$ $a = \dfrac{-34z + 69}{-24z + 36}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{34z - 69}{24z - 36}$